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medium
The slope of the tangent to the curve $y = ln\, (cos\,x)$ a $x = \frac{3\pi}{4}$ is
A
$1$
B
$-1$
C
$\ln \,\sqrt 2 $
D
$\frac{1}{{\sqrt 2 }}$
Solution
$y = \ell n(\cos x)$
$\quad \frac{d y}{d x}=\frac{1}{\cos x} \times(-\sin x)$
$\quad=-\tan x$
at $\quad x=\frac{3 \pi}{4}$
$\quad\left(\frac{d y}{d x}\right)_{x=3 \pi / 4}=-\tan 3 \pi / 4=1$
Standard 11
Physics
